Question

若x>1，求y=(x^2-x+1)/(x-1)最小值

请大家帮帮忙啦~~谢谢啦~~过程请具体一些，因为我不会做~~

Answer 1

y=(x^2-2x+2)/(2x-2)
=[(x-1)^2+1]/2(x-1)
(分子分母同除以x-1)
=[(x-1)+1/(x-1)]/2
x＞1,x-1>0
y>=2*(1/2)√(x-1)*[1/(x-1)]
(当且仅当x-1=1/(x-1)时取到等号）
=1
y最小值=1

Answer 2

解答：
y=(x^2-x+1)/(x-1)=[x(x-1)+1]/(x-1)
=x+1/(x-1)=x-1
+
1/(x-1)
+1
由于x>1,则x-1>0
所以y=x-1
+1/(x-1)
+1
>=1+1=2
也即最小值为2.
完毕。